A secondary college is required to survey students' parents to determine the level of satisfaction with the school. A stratified random sample of 50 students is taken from the school population of 755 students. How many should be chosen from each year level if the enrolments are as shown below.
Year 7: 222 Year 8: 237 Year 9: 149 Year 10: 147
With this question I have responded by dividing every students in each year level by the total school population of 755 and then multiplying the result by 50.
222/755*50=14.70198675 These were the results that I received.
237/755*50=15.69536424 However since I was working out the number
149/755*50=9.867549669 of people it were necessary for me to round
147/755*50=9.735099338 to the nearest whole number (see below).
Year 7= 15 Year 8= 16 Year 9= 10 Year 10= 10
As you can see due to the rounding up or down to the nearest whole number 51 students were taken instead of 50. To counter act this, the book (where I got the puzzling question from) rounded 9.7350993... to 9 instead of 10.
Is this what you do in this situation? Round one of the numbers the wrong way? If so, how do I know which number to round the wrong way? If not, tell me the correct way of doing this. It is too frustrating...